In existing studies on neural networks (NNs) stabilization, stochastic disturbances are typically regarded as negative factors. In contrast, this paper systematically explores the positive role of stochastic disturbances in the stabilization of NNs and proposes a novel finite-time noise feedback control method. By rationally utilizing stochastic disturbances, the originally unstable fuzzy memristive NNs with reaction-diffusion components achieve finite-time stochastic stabilization. Meanwhile, some less conservative finite-time stabilization criteria are proposed, eliminating the requirement in classical criteria that Lyapunov function’s differential operator must be strictly negative. The novel criteria not only extend the application scope of existing stochastic stabilization from exponential stabilization to finite-time case, but also elaborately explore the relationship between noise intensity and the convergence speed of the system. Finally, the effectiveness of derived results is verified through simulation.

This article focuses on the problem of $N$ -step model predictive control (MPC) under a mixed time/event-triggered encoding-decoding strategy for polytopic uncertain systems with hard constraints. A staged requirements-dependent mixed time/event-triggered mechanism (MTEM) is proposed. When the system state is outside the terminal constraint set (TCS), the time-triggered pattern is implemented to meet the staged requirement of improving control performance. When the system state is in the TCS, an event-triggered pattern is used to fulfill the staged requirement of conserving resources. The event-triggered pattern contains an adaptively adjusting variable related to the "distance" of the system state from the TCS core, which helps meet the relative staged requirements in the TCS. The staged requirements-dependent MTEM-based encoding-decoding strategy improves the communication security while saving computational resources for encoding and decoding, as well as network resources. Based on two offline optimization problems (OPs), the TCS and the approximate robust one-step sets are designed, respectively. The control laws outside the TCS are obtained by an online OP. A mixed time/event-triggered encoding-decoding-based $N$ -step MPC algorithm is proposed based on three OPs. The algorithm's feasibility and the input-to-state stability of the closed-loop system are analyzed. Two examples are presented to illustrate the effectiveness and superiority of the proposed MTEM and MPC algorithm in saving resources while ensuring control performance.

This article develops a robust economic model predictive control (EMPC) scheme for load frequency control (LFC) in multiarea smart grids with load disturbances. The proposed approach integrates the optimization of the cost and the utilization efficiency of network resources within a single EMPC framework. An economic cost function, including the generation cost and the LFC cost, is designed to minimize the involved costs. To optimize the utilization efficiency of network resources while maintaining satisfactory control performance, a new dynamic memory event-triggered mechanism (DMETM) is designed. By introducing a dynamic variable and an adaptively adjusting variable, the proposed DMETM adaptively adjusts triggering conditions using historical triggering information, thereby conserving network resources and reducing communication burden. A “min–max” EMPC optimization problem (OP) is developed, and it is transformed into an auxiliary OP based on linear matrix inequalities. The recursive feasibility of the auxiliary OP is proved, and the closed-loop system is also proven to satisfy input-to-state practical stability, guaranteeing robustness against the load disturbances. At last, a case study on a three-area smart grids verifies the effectiveness and the advantages of the proposed DMETM-based EMPC scheme and demonstrates its potential in enhancing the optimization of the economic cost and the utilization efficiency of network resources.

This paper is dedicated to addressing the event-triggered$H_{\infty }$control problem for interval type-2 fuzzy systems. A weakly constrained event-triggered functional is proposed by incorporating the event-triggering variable and$H_{\infty }$performance index, which relaxes the restrictions imposed on Lyapunov functionals in existing sampled-data control studies. This functional also provides a graceful event-triggered$H_{\infty }$analysis framework that avoids the use of the$S$-procedure. Then, the Lyapunov matrices in the functional are set to be aperiodic sampling-dependent, thereby further reducing the conservatism of the criteria. Furthermore, a basic-inequality-based method is provided to handle the imperfect premise matching between the fuzzy system and the fuzzy controller in interval type-2 fuzzy systems, avoiding the previous introduction of additional free matrices and extra constraints. Thereafter, the fuzzy controller design method is given, and the aperiodic sampling-based static/dynamic event-triggered control is effectively implemented. Ultimately, two case studies validate the effectiveness of the proposed approaches and demonstrate their ability to achieve superior event-triggered control effects compared with the existing literature.

In this article, the problem of multistep model predictive control (MPC) under a mixed time/event-triggered mechanism (MTEM) is investigated for fuzzy systems with hard constraints. To improve its flexibility in adjusting releases, this MTEM incorporates the information from the fuzzy membership functions and the terminal constraint set (TCS). In the online control unit, the time-triggered way is first implemented to steer the system state into the TCS quickly, and then in the offline control unit, the involved event-triggered pattern plays its role in conserving resources while ensuring the control performance. Two offline optimization problems (OPs) are presented to design the TCS and the approximate robust one step sets, respectively, and an online OP is given to design the control laws to steer the system state into TCS. Based on these three OPs, we propose an MTEM-based multistep fuzzy MPC algorithm and demonstrate the feasibility of the algorithm together with the input-to-state stability of the closed-loop system. Three examples are given to verify the effectiveness of the proposed method and its superiority in saving communication and computing resources while ensuring control performance.

This article investigates the multistep model predictive load frequency control problem for multiarea smart grids (MASGs) with wind power and air conditioning loads under false data injection attack, where a control performance standards (CPSs)-dependent dynamic event-triggered mechanism (DETM) is considered to manage the data transmission. The CPSs-dependent DETM contains an adaptive adjustment variable related to two CPSs on the frequency deviation and area control error, which helps it to effectively reduce unnecessary transmission of data packets while promising the required frequency and tie-lie power of the MASGs. Two off-line optimization problems (OPs) are applied to design the terminal constraint set (TCS) and the approximate one step sets, respectively. The control laws designed by an online OP are utilized outside of the TCS. A CPSs-dependent DETM-based multistep MPC algorithm is proposed on the basis of the three OPs. The analyses of the feasibility of the algorithm and the stability of the closed-loop system are given. The effectiveness and superiority of the designed CPSs-dependent DETM and dynamic event-based multistep MPC algorithm are verified in two case studies of two-area and three-area smart grids.

The event-triggered model predictive control (MPC) problem is addressed for polytopic uncertain systems. A new dynamic event-triggered mechanism (DETM) with a bounded dynamic variable and a time-varying threshold is proposed to manage measurement data packet releases. The dynamic output-feedback MPC issue is detailed as a "min-max" optimization problem (OP) with an objective function over an infinite horizon, where the hard constraint on the predictive control is required. By applying a Lyapunov-like function containing the bounded dynamic variable, an auxiliary OP constrained by several matrix inequalities is proposed, and the design methods of the output-feedback gains are provided if this auxiliary OP is feasible. The designed MPC controller ensures that the closed-loop system is input-to-state practically stable. Two examples including an event-triggered DC motor are given to illustrate the validity of the developed MPC algorithm. Simulation results verify that the proposed DETM has advantages over some existing triggering mechanisms in decreasing the consumption of resources while meeting the required performance.

The focus of this paper is on maintaining the stability and stabilization of Takagi-Sugeno fuzzy systems under conditions of time-delay and sampled-data control. The objective is to introduce stability analysis and synthesis methods that are less conservative. First, a novel sampling point-dependent looped-functional with augmented integral terms is constructed. Then, we propose a matrix-separation-based inequality to obtain a compact estimation for the augmented integral term. Stability and stabilization results with reduced conservatism are obtained based on the above innovative method. The superiority and efficacy of the proposed methods are ultimately demonstrated through the presentation of three examples.

This article investigates the efficient model predictive load frequency control problem for multiarea power systems, where the measured state is transmitted under a new dynamic event-triggered mechanism (DETM) with hybrid variables. By applying$H_{2}$/$H_{\infty }$performance index, a DETM-based efficient model predictive control (EMPC) method is presented. This EMPC issue is described as a “min-max” optimization problem (OP) with hard constraints on system state. By utilizing a Lyapunov function with internal dynamic variable, an offline auxiliary OP with constraints of matrix inequalities is put forward to optimize the feedback gain and the weighting matrix of the DETM. Another offline OP is also proposed to maximize the size of initial feasible region (IFR). To steer the augmented state in IFR into the terminal constraint set and improve the control performance, a sequence of admissible control is implemented whose perturbation parameters are designed by solving an online OP. A case study on a three-area power system demonstrates the validity and superiority of the designed DETM and dynamic event-based EMPC algorithm.

This article investigates the problem of dynamic event-triggered finite-time$H_{\infty }$state estimation for a class of discrete-time nonlinear two-time-scale Markov jump complex networks. A hybrid adjusting variables-dependent dynamic event-triggered mechanism (DETM) is proposed to regulate the releases of measurement outputs of a node to a remote state estimator. Such a DETM contains both an additive dynamically adjusting variable (DAV) and a multiplicative adaptively adjusting variable. The aim is to design a DETM-based mode-dependent state estimator, which guarantees that the resultant error dynamics is stochastically finite-time bounded with$H_{\infty }$performance. By constructing a mode-dependent Lyapunov function with multiple DAVs and a singular perturbation parameter associated with time scales, a matrix-inequalities-based sufficient condition is derived, the feasible solutions of which facilitate the design of the parameters of the state estimator. The validity of the designed state estimator and the superiority of the devised DETM are verified by two examples. It is verified that the devised DETM is capable of saving network resources and simultaneously improving the estimation performance.

The issue of fault detection and isolation (FDI) under an event-triggered mechanism (ETM) is investigated for switched linear systems. An improved dynamic ETM (DETM), which includes some existing ETMs as special cases, is devised. Such a DETM contains two internal dynamic variables (IDVs), the mode information and seven adjustable parameters, and thus is flexible in adjusting the data packet transmissions to save network resources. The aim is to design a fault detection (FD) filter (FDF) and fault isolation filters (FIFs) such that the resultant filtering error systems are exponentially stable with prescribed exponential$H_{\infty }$performance. A new Lyapunov function, which depends on the switching mode and two IDVs, is constructed. By utilizing the Lyapunov method and the average dwell time approach, sufficient conditions are derived to guarantee the existence of the desired FDF and FIFs, whose design methods are given accordingly. A numerical example is provided to demonstrate the effectiveness of the FDI method and the superiority of the devised DETM in reducing the waste of network resources while maintaining the FD filtering performance.

The issue of finite-time$H_{\infty }$state estimation is studied for a class of discrete-time nonlinear two-time-scale complex networks (TTSCNs) whose measurement outputs are transmitted to a remote estimator via a bandwidth-limited communication network under the stochastic communication protocol (SCP). To reflect different time scales of state evolutions, a new discrete-time TTSCN model is devised by introducing a singular perturbation parameter (SPP). For the sake of avoiding/alleviating the undesirable data collisions, the SCP is adopted to schedule the data transmissions, where the transition probabilities involved are assumed to be partially unknown. By constructing a new Lyapunov function dependent on the information of the SCP and SPP, a sufficient condition is derived which ensures that the resulting error dynamics is stochastically finite-time bounded and satisfies a prescribed$H_{\infty }$performance index. By resorting to the solutions of several matrix inequalities, the gain matrices of the state estimator are given and the admissible upper bound of the SPP can be evaluated simultaneously. The performance of the designed state estimator is demonstrated by two examples.

Based on a hidden Markov model (HMM), the issue of fault detection (FD) is investigated for singularly perturbed systems with their measurements transmitted over a bandwidth-limited communication network. A homogeneous Markov chain is adopted to model packet dropouts and time delays simultaneously, whose mode transition probabilities are assumed to be partially unknown. The discrepancies between the Markov modes and their observed ones have been noted, which are reflected by a hidden Markov process. An HMM-based FD filter (FDF) is aimed to be designed such that the stochastic stability and prescribed H∞performance are ensured for the resulting filtering error dynamics of FD. A new Lyapunov-Krasovskii functional is constructed, which is with the Markov mode and the singular perturbation parameter (SPP). With the aid of up-to-date techniques in handing time delays, a sufficient condition based on linear matrix inequalities (LMIs) is derived which provides a design scheme of such an FDF. The FDF parameters are given and the SPP's admissible bounds are evaluated when the LMIs have feasible solutions. The performance of the designed FDF is demonstrated by two examples.

This paper deals with the finite-horizon quantized H∞state estimation problem for a class of discrete timevarying genetic regulatory networks with quantization effects under stochastic communication protocols (SCPs). To better reflect the data-driven flavor of today's biological research, the network measurements (typically gigabytes in size by highthroughput sequencing technologies) are transmitted to a remote state estimator via two independent communication networks of limited bandwidths. To lighten the communication loads and avoid undesired data collisions, the measurement outputs are quantized and then transmitted under two SCPs introduced to schedule the large-scale data transmissions. The purpose of this paper is to design a time-varying state estimator such that the error dynamics of the state estimation satisfies a prescribed H∞performance requirement over a finite horizon in the presence of nonlinearities, quantization effects, and SCPs. By utilizing the completing-the-square technique, sufficient conditions are derived to ensure the H∞estimation performance and the parameters of the state estimator are designed by solving coupled backward recursive Riccati difference equations. A numerical example is given to illustrate the effectiveness of the design scheme of the proposed state estimator.

This paper investigates the H∞state estimation problem for a class of discrete-time nonlinear singularly perturbed complex networks (SPCNs) under the Round-Robin (RR) protocol. A discrete-time nonlinear SPCN model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter (SPP). The network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the RR protocol with hope to avoid the undesired data collision. The error dynamics of the state estimation is governed by a switched system with a periodic switching parameter. A novel Lyapunov function is constructed that is dependent on both the transmission order and the SPP. By establishing a key lemma specifically tackling the SPP, sufficient conditions are obtained such that, for any SPP less than or equal to a predefined upper bound, the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed H∞performance requirement. Furthermore, the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities, and the upper bound of the SPP is then evaluated in the feasibility of these matrix inequalities. Moreover, the corresponding results for linear discrete-time SPCNs are derived as corollaries. A numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme.

This letter describes the improvement of two methods of detecting high-frequency oscillations (HFOs) and their use to localize epileptic seizure onset zones (SOZs). The wavelet transform (WT) method was improved by combining the complex Morlet WT with Shannon entropy to enhance the temporal-frequency resolution during HFO detection. And the matching pursuit (MP) method was improved by combining it with an adaptive genetic algorithm to improve the speed and accuracy of the calculations for HFO detection. The HFOs detected by these two methods were used to localize SOZs in five patients. A comparison shows that the improved WT method provides high specificity and quick localization and that the improved MP method provides high sensitivity.